Question

If `int (3ax)/(b^2 + c^2x^2) = A log |b^2 + c^2x^2| + K`, then the value of A is ______.

Options

• 3a

• `(3a)/(2b^2)`

• `(3a)/(b^2c^2)`

• `(3a)/(2c^2)`

Answer 1

If `int (3ax)/(b^2 + c^2x^2) = A log |b^2 + c^2x^2| + K`, then the value of A is `underlinebb((3a)/(2c^2))`.

Explanation:

Let I = `int (3ax)/(b^2 + c^2x^2)dx`

Put u = b² + c²x², So du = 2c²x dx

Then,

I = `(3a)/(2c^2) int (du)/u`

I = `(3a)/(2c^2) log |b^2 + c^2x^2| + K`

Hence, A = `(3a)/(2c^2)`.